# The GALAH survey and Gaia DR2: Linking ridges, arches and vertical waves in the kinematics of the Milky Way

## TL;DR

This study links Gaia DR2 star kinematic patterns with phase mixing of spiral arms, revealing ridges and arches as surfaces of constant energy, and demonstrates their formation through N-body simulations involving satellite perturbations.

## Contribution

It shows that phase mixing of spiral arms explains the observed ridges and arches in Milky Way star kinematics, highlighting their energy and angular momentum properties and coupling between planar and vertical motions.

## Key findings

- Ridges are present in multiple kinematic and chemical abundance maps.
- Ridges correspond to surfaces of constant orbital energy or angular momentum.
- Simulations show ridges can form in both isolated and satellite-perturbed galactic discs.

## Abstract

Gaia DR2 has revealed new small-scale and large-scale patterns in the phase-space distribution of stars in the Milky Way. In cylindrical Galactic coordinates $(R,\phi,z)$, ridge-like structures can be seen in the \vphiR{} plane and asymmetric arch-like structures in the \vphivR{} plane. We show that the ridges are also clearly present when the third dimension of the \vphiR{} plane is represented by $\langle z \rangle$, $\langle V_z \rangle$, $\langle V_R \rangle$, $\langle$[Fe/H]$\rangle$ and $\langle[\alpha/{\rm Fe}]\rangle$. The maps suggest that stars along the ridges lie preferentially close to the Galactic midplane ($|z|<0.2$ kpc), and have metallicity and $\alpha$ elemental abundance similar to that of the Sun. We show that phase mixing of disrupting spiral arms can generate both the ridges and the arches. It also generates discrete groupings in orbital energy $-$ the ridges and arches are simply surfaces of constant energy. We identify 8 distinct ridges in the \gaia{} data: six of them have constant energy while two have constant angular momentum. Given that the signature is strongest for stars close to the plane, the presence of ridges in $\langle z \rangle$ and $\langle V_z \rangle$ suggests a coupling between planar and vertical directions. We demonstrate, using N-body simulations that such coupling can be generated both in isolated discs and in discs perturbed by an orbiting satellite like the Sagittarius dwarf galaxy.